#geodesic

But there is a long way toward the modern statement: “on any complete abstract Riemannian manifold of ≥0 curvature of any dimension, curvature is the quotient of its universal covering by a discrete group of isometries.”

Marcel Berger, Riemannian Geometry during the Second Half of the Twentieth Century

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Harriss Geodesics

Buckminster Fuller

According to General Relativity, matter warps spacetime, and this warping of spacetime is what we perceive as gravity. Gravitation isn't actually a force, it's a consequence of motion through curved spacetime.

Earths elliptical orbit around the sun is actually a straight line in curved spacetime, this is called a geodesic, a straight line on a curved surface.

So, the sun, for example, curves spacetime (matter telling space how to bend) and objects, like the earth, orbit along that curve (space telling matter how to move).

If matter didn't curve spacetime then nothing would orbit anything and gravity would be nonexistent.